Question

# A stone is dropped from the top of a tower and travels $44.5\mathrm{m}$in the last second of its journey. The height of the tower is

A

$44.1m$

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B

$49m$

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C

$78.4m$

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D

$72m$

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Solution

## The correct option is A $44.1m$Find the height of the tower.Explanation of correct option:Consider that the tower is $h$ in total height and that it takes $t$ to descend to the ground.The height is given as:$\mathrm{h}=\frac{1}{2}{\mathrm{gt}}^{2}...\left(i\right)$The height before last seconds is given as:$\mathrm{h}-24.5=\frac{1}{2}\mathrm{g}\left(\mathrm{t}-1{\right)}^{2}\left[\because \mathrm{from}\left(\mathrm{i}\right)\right]\phantom{\rule{0ex}{0ex}}⇒\frac{1}{2}\mathrm{gt}{}^{2}-24.5=\frac{1}{2}\mathrm{g}\left(\mathrm{t}{\right)}^{2}+\frac{1}{2}\mathrm{g}-\mathrm{gt}\phantom{\rule{0ex}{0ex}}⇒\mathrm{t}=3\mathrm{s}$Insert the value of $\mathrm{t}=3$ in the equation $\left(i\right)$:$\begin{array}{rcl}\mathrm{h}& =& \frac{1}{2}×9.8\left(3{\right)}^{2}\\ & ⇒& \mathrm{h}=44.1\mathrm{m}\end{array}$Hence, the height of the tower is $44.1\mathrm{m}$.Hence, Option A is the correct option.Explanation of incorrect option:Since, the height of the tower is $44.1\mathrm{m}$ which is determined above is not equal any of the values mentioned in Option A, Option B and Option C Thus, Option A Option B and Option C are incorrect option.Hence,Option A is the correct option.

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